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A210877 Triangle of coefficients of polynomials v(n,x) jointly generated with A210876; see the Formula section. 4
1, 0, 3, 0, 3, 4, 0, 2, 8, 5, 0, 2, 6, 17, 6, 0, 2, 5, 18, 31, 7, 0, 2, 5, 14, 47, 51, 8, 0, 2, 5, 13, 41, 107, 78, 9, 0, 2, 5, 13, 35, 115, 218, 113, 10, 0, 2, 5, 13, 34, 98, 296, 407, 157, 11, 0, 2, 5, 13, 34, 90, 276, 695, 709, 211, 12, 0, 2, 5, 13, 34, 89, 244, 750 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n>2, each row begins with 0 and ends with n+1.  If the term in row n and column k is denoted by U(n,k), then U(n,n-2)=A105163(n-1).

Row sums: A000225 (-1+2^n)

Alternating row sums:  A137470

Limiting row:  0,2,5,13,34,89,..., even-indexed Fibonacci numbers

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..74.

FORMULA

u(n,x)=x*u(n-1,x)+v(n-1,x)+1,

v(n,x)=x*u(n-1,x)+x*v(n-1,x)+x,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First six rows:

1

1...2

1...1...3

1...1...3...4

1...1...2...8...5

1...1...2...6...17...6

First three polynomials v(n,x): 1, 1 + 2x, 1 + x + 3x^2

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;

u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;

v[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + x;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A210876 *)

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A210877 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A000225 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A077973 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A137470 *)

CROSSREFS

Cf. A210876, A208510.

Sequence in context: A210485 A111815 A281269 * A127753 A197736 A073367

Adjacent sequences:  A210874 A210875 A210876 * A210878 A210879 A210880

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 30 2012

STATUS

approved

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Last modified May 24 14:49 EDT 2019. Contains 323532 sequences. (Running on oeis4.)